In this paper set optimization problems with three types of set order relations are concerned. We introduce various types of Levitin–Polyak (L P) well-posedness for set optimization problems and survey their relationships. After that, sufficient and necessary conditionsfor thereference problems to be L P well-posed are given. Furthermore,
using the Kuratowski measure of noncompactness, we study characterizations of wellposedness for set optimization problems. Moreover, the links between stability and L P well-posedness of such problems are established via the study on approximating solution mappings. Tools and techniques used in this study and our results are different
from existing ones in the literature.